Question

Which is the correct order for a given number $\alpha$ in increasing order.

• A. ${\log }_2\alpha ,{\log }_e\alpha ,{\log }_3\alpha ,{\log }_{10}\alpha$
• B. ${\log }_{10}\alpha ,{\log }_3\alpha ,{\log }_e\alpha ,{\log }_2\alpha$
• C. ${\log }_{10}\alpha ,{\log }_e\alpha ,{\log }_2\alpha ,{\log }_3\alpha$
• D. ${\log }_3\alpha ,{\log }_e\alpha ,{\log }_2\alpha ,{\log }_{10}\alpha$

Answer 1

Answer: (A)

${\log }_2\alpha ,{\log }_e\alpha ,{\log }_3\alpha ,{\log }_{10}\alpha$

We know that, greater the value of base lesser is the value of the logarithm

Also, $10<3<e\left(2.71\right)<2$

$\therefore$ For any positive number $\alpha$,

${log}_2\alpha >{log}_e\alpha >{log}_3\alpha >{log}_{10}\alpha$